Petr Cech has completed his £10m transfer across London to Arsenal, drawing a line under a glittering 11-year career at Chelsea with an admission that “life doesn’t always turn out the way you think it will”.

The Czech international, who claimed 13 major trophies including the Champions League while at Stamford Bridge, conceded he had slipped behind Thibaut Courtois in the pecking order last season and, with little prospect of that situation changing, decided it was time for a new start.

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The 33-year-old spoke to Roman Abramovich and stressed his desire to remain in the Premier League despite interest from Paris Saint-Germain, with the owner duly sanctioning the move to a direct rival, albeit reluctantly, out of respect for Cech’s eye-catching contribution while at Chelsea.

The goalkeeper has signed a four-year contract worth a basic £100,000 a week and may confront his former team-mates in the Community Shield at Wembley on 2 August. Arsenal are due at Stamford Bridge in mid-September. “I thought this would never happen, but it is time for me to say goodbye to Chelsea Football Club: the club I have lived every single minute for since joining in July, 2004, the club in which I thought I’d hang my gloves and boots one day and finish my career,” he wrote in an open letter published on social media. “But life doesn’t always turn out the way you think it will.

“It has been an incredible journey with so many highs and not many lows. We have managed to win every single English trophy as well as the Europa League and the biggest of all – the Champions League. Looking back at all the achievements, including our first ever league double in 2010, back to back titles in 2005 and 2006, and multiple Premier League and FA Cup wins, I couldn’t be more proud. As a team, we made history together.

“Last summer, things changed and I understood I was no longer the first-choice keeper, but I felt it was not the right time for me to go. During the season it became clear that my situation would not improve and, as I know I am not at the stage of my career where I want to be on the bench, I made my decision to move on and look for new challenges.”

Cech, who ended with 228 clean sheets from his 494 games, featured only seven times in the Premier League last season, with the champions winning all of them and the keeper conceding only twice, but Courtois’ position as the long-term No1 remained clear. Chelsea have seen a £6m bid for the Stoke goalkeeper Asmir Begovic rejected but are expected to return with an improved offer for a player who is entering the final year of his contract at the Britannia Stadium. Stoke may attempt to take a player on loan from Stamford Bridge as part of the deal but that is unlikely to be Victor Moses.

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“The limited playing time gave me the chance to refresh and rest mentally as well as made me realise just how much I enjoy playing football at the highest level, because I missed it badly every game day I was not involved,” said Cech. “I have the same commitment to football, the same motivation and the same hunger for success as I had at the beginning of my career. I love the challenges brought by the top quality players you face while playing in the Premier League: simply the best and the most challenging league in the world. That’s why I spoke to Mr Abramovich about me staying in the Premier League, and I’d like to thank him from the bottom of my heart for his support in this matter.”

Arsenal, who have dropped their interest in Juventus’ Arturo Vidal, may now sanction David Ospina’s move to Fenerbahce. Wojciech Szczesny, who will compete with Cech for a first-team place next season, welcomed the older man to the club on his Instagram account and is intent on remaining at the Emirates Stadium. “Petr Cech is a player I have admired for a long time and I am very pleased that he has decided to join us,” said the manager, Arsène Wenger. “He has proven over many seasons that he is one of the outstanding keepers in the world and he will add great strength to our squad.”

Cech added: “When Arsène spoke to me about his ambitions for this club, and how he saw me as part of this team, the decision was clear.”

• This article was amended on 30 June 2015 because Petr Cech joined Chelsea Football Club in 2004, not 2014 as an earlier version said.